What is the sum of the geometric sequence -3, 18, -108,
if there are 8 terms?

Answer:

d

Step-by-step explanation:

the opposite angles of a cyclic quadrilateral sum to 180° , that is

∠ ABD + ∠ ACD = 180°

∠ ABD + 48° = 180° ( subtract 48° from both sides )

∠ ABD = 132°

From my analysis, the answer is likely to be D. I don't have a formula to prove it though.

Answer: 78 degrees.

Step-by-step explanation:

The other guy is wrong don't listen to him.

Using a system of equations, it is found that there were 4,000 children tickets sold.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given by:

The attendance at the amusement park is 5,000 attendees, hence:

x + y = 5000 -> y = 5000 - x.

Considering the cost of parking and that the total money earned by the park is $100,000, we have that:

15x + 40y = 100000

Applying the multiplication of the matrices, these equations are the same that the system gives. Replacing the second equation into the first:

15x + 40(5000 - x) = 100000

25x = 100000

x = 100000/25

x = 4000.

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x / 3 ≤ -6

---Multiply both sides by 3 to cancel out the denominator on the left side

x ≤ -18

Hope this helps!

Answer:

If the equation is 19-5=3z-11 then the value of z is 15/3.

Given an equation in terms of z is 19-5=3z-11.

We are required to find the value of variable z which exist in equation.

Equation is like a  relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.

The value of z can be find as under:

19-5=3z-11

4=3z-11

3z=4+11

3z=15

z=15/3

Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.

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Answer:

(4, 1 )

Step-by-step explanation:

x = 3y + 1 → (1)

2x + 4y = 12 → (2)

substitute x = 3y + 1 into (2)

2(3y + 1) + 4y = 12

6y + 2 + 4y = 12

10y + 2 = 12 ( subtract 2 from both sides )

10y = 10 ( divide both sides by 10 )

y = 1

substitute y = 1 into (1)

x = 3(1) + 1 = 3 + 1 = 4

solution is (4, 1 )

Answer:

$525

Step-by-step explanation:

We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:

[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]

To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:

525 * 0.36 = 189

525 - 189 = 336

Modeling the first formula gives us:

525 - (0.36 * 525) = 336

525 - 189 = 336

Answer:   100 square cm

Step-by-step explanation:   the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.

Answer: 104

Step-by-step explanation:

area of trangle =33 because 6*11/2=33

area of rectangle 9*7=63

area of rectangle  2*2=4

33+63+4=100^2

Answer:

The answer is: (x,y) = (-2,5)

u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1). This can be obtained by simplifying the equation and taking w to one side of the equation with other constants.

Simplifying an equation can be done by using the following steps:

Here it is given that the equation is,

⇒ u - 5= - 4(w - 1)

We have to find an equation in which w is taken to one side of the equation with other constants.

First by adding both side of the equation with 5 we get,

⇒ u - 5 + 5 = - 4(w - 1) + 5

By opening the bracket we get,

⇒ u = - 4w + 4 + 5

Finally by adding the constants we get,

⇒ u = - 4w + 9

Hence u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1).

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Answer:  C

Step-by-step explanation: the other two options are both wrong, 0.13 is larger than 0.125 and she did order by volume per fish.

Answer:

135 is correct answer of this question

The standard form of the given quadratic equation in  factored form is

(x+2) (x-6) = x²-4x-12

(x-4) (x+3) = x²-x-12

(x-12) (X+1) = x²-11x-12

(x-3) (x+4) = x²+x-12

what are quadratic equations?

A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero

To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.

f(x) = (x+2) (x-6)

x²+2x-6x-12

x²-4x-12

similarly, the standard form of equations 2,3 and 4 are :

(x²-x-12)

(x²-11x-12)

(x²+x-12)

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Answer:

B, D, A, C

Step-by-step explanation:

f(x) = (x + 2)(x – 6)

✔ B

f(x) = (x – 4)(x + 3)

✔ D

f(x) = (x – 12)(x + 1)

✔ A

f(x) = (x – 3)(x + 4)

✔ C

Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:

(8.34%, 17.66%).

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the estimate and the sample size are given, respectively, by:

[tex]\pi = 0.13, n = 200[/tex]

Hence the bounds of the interval are:

As a percentage, the interval is:

(8.34%, 17.66%).

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Answer:

x = 3

Step-by-step explanation:

Given the information from the question, we can deduce that:

3 - x = x - 3

Now our goal here is to find x.

3 - x = x -3

3 - x - 3  = x - 3 - 3

- x = x - 6

- x - x = x - 6 - x

- 2x = - 6

x = [tex]\frac{-6}{-2}[/tex] = 3

Answer: 3

Step-by-step explanation: The only value for x in which 3 - x is the same as x - 3 is where x does not affect the value of 3 whatsoever. We can also set this up algebraically to find this out algebraically.

x - 3 = 3 - x

Adding 3 to both sides, we have

x = 6 - x

Adding x to both sides we have

2x = 6

Dividing by 2 from both sides, we get

x = 3

The polynomial that should be subtracted from the dividend first is; x³ + 2x²

The long division we are given is;

        __________

x + 2 ) x³ + 3x² + x

Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².

Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;

(x + 2) * (x²) = x³ + 2x²

Thus, the polynomial to be subtracted is x³ + 2x²

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The two stadiums are 2,871 meters

A blimp    = point A

stadium 1  = point B

stadium 2 = point C

height of the blimp ,  AD = 1600

depression angle of stadium 1 , ∠y = 71.7°

depression angle of stadium 2 , ∠x = 25.2°

distance between the two stadiums  = d

So, it forms 2 triangles  ABD and ACD,

Using the trigonometric ratios,

tan θ = Altitude / Base

DC = AD × tan (90° - x)

= 1600 × tan( 90° - 25.2° )

= 1600 × cot(25.2°)

= 1600 × 2.13

DB = AD × tan (90° - y)

= 1600 × tan( 90° - 71.7° )

= 1600 × cot(71.7°)

= 1600 × 0.33

∴ d = DC - DB

     = 1600 * [ tan( 90° - 25.2° ) - tan( 90° - 71.7° ) ]

    = 2,871 meters

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Answer:

27/31

Step-by-step explanation:

FIrst, construct a ratio. Isabelle needs 3/10 red to make 31/30 purple. So, we can divide red by purple to form a fraction to determine how much red paint for 1 fluid oz of purple. (3/10)/(31/30)=(9/30)/(31/30)=9/31. For every 1 oz of purple, we need 9/31 oz of red. Because we found how much red paint for 1 oz purple paint, we simply multiply by 3 to find how much red paint for 3 fluid oz of purple paint. (9/31)*3=27/31

32 bottles are needed to poured 4 gallons of chocolate milk.

The correct option is D.

A closed surface's volume, which is expressed as a scalar quantity, measures how much three-dimensional space is enclosed. The area that a material or 3D object takes up or contains, for instance. The SI-derived cubic metre is a common unit for quantifying volume quantitatively.

Pints to Gallons Ratio: 1:8

Permit x bottles to be present.

There are x bottles required for 4 gallons of chocolate milk.

Because of the direct proportion

4/x = 1/8

x = 4 x 8

x = 32

As a result, 32 bottles are required.

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Answer:

option c

Step-by-step explanation:

option c is a correct answer

Answer:

Gustavo used a simulation where the data is quantitative’

Answer:

m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131

m∠RST = 2x = 2(14) = 28

m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103

Step-by-step explanation:

m∠RSU = m∠RST + m∠TSU

10x - 9 = 2x + (2x + 75)

10x - 9 = 2x + 2x + 75

10x - 9 = 4x + 75

-4x +9     -4x  +9

      6x = 84

         x = 14

m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131

m∠RST = 2x = 2(14) = 28

m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103

Answer:

A

Step-by-step explanation:

a.  The expressions for c and d in terms of a and b are

b.  The inverse of (2,1) is (13/15, -4/15)

The question has to do with binary operation.

A binary operation is a rule of mathematical operation on two sets of elements defined on a given set.

Since The operation * is defined over the set of ordered pairs by (a,b)*(c,d)=(ac-bd,ad+bc) for all (a,b),(c,d)€R given that the inverse of (a,b) is (c,d).

Let (e, e') be the identity element.

We know that for any binary operation * on a given set, a*e = a where e is the identity element.

So,  (a,b)*(e,e') =  (a,b)

So, (a,b)*(c,d) = (ac - bd, ad + bc)

(a,b)*(e,e') = (ae - be, ae' + be')

Since  (a,b)*(e,e') =  (a,b)

(ae - be, ae' + be') = (a, b)

So,

e = a/(a - b) and e' = b/(a + b)

So, (e, e') = (a/(a - b), b/(a + b))

Also, for any binary operation * under a given set a*a⁻¹ = e where a⁻¹ = inverse of a.

Since (c,d) is the inverse of (a,b), we have that

(a,b)*(c,d) = (e, e')

So, (a,b)*(c,d) = (ac - bd, ad + bc)

=  (a/(a - b), b/(a + b))

So,

From (3), c = bd/a + 1/(a - b)

Substituting c into (4), we have

ad + bc = b/(a + b)  

ad + b[bd/a + 1/(a - b)] = b/(a + b)  

ad + b²d/a + b/(a - b) = b/(a + b)  

ad + b²d/a = b/(a + b) -  b/(a - b)]

(a + b²/a)d = b[1/(a + b) -  1/(a - b)]

[(a² + b²)/a]d = b[a - b - (a + b)]/(a - b)(a + b)

[(a² + b²)/a]d = b[a - b - a - b)]/(a - b)(a + b)

[(a² + b²)/a]d = b(-2b)/(a² - b²)

d = -2ab²/[(a² - b²)(a² + b²)]

d = -2ab²/(a⁴ - b⁴)

Substitutind d into c, we have

c = bd/a + 1/(a - b)

c = -2ab³/(a⁴ - b⁴)a + 1/(a - b)

c = -2b³/(a⁴ - b⁴) + 1/(a - b)

So, the expressions for c and d in terms of a and b are

Since (c,d) is the inverse of (a,b) is

So, with a = 2 and b = 1, c = -2b³/(a⁴ - b⁴) + 1/(a - b)

= -2(1)³/(2⁴ - 1⁴) + 1/(2 - 1)

= -2/(16 - 1) + 1/1

= -2/15 + 1

= (-2 + 15)/15

= 13/15

So, with a = 2 and b = 1, d = -2ab²/(a⁴ - b⁴)

= -2(2)(1)²/(2⁴ - 1⁴)

= -4(1)/(16 - 1)

= -4/15

So, the inverse of (2,1) is (13/15, -4/15)

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The probability that the machine produces fewer than 3 defective widgets in a production run of 75 items is 0.041.

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 3 widgets.

It has a 0.12 defective rate.

Defective rate fewer than 3

Total Probability = P of 2 defective + P for 1 defective

Total Probability = 2/74 + 1/73

Total Probability ≈ 0.04072565716

Total Probability ≈ 0.041

Therefore, the required probability for fewer than 3 defective rate is 0.041

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[tex](-7+9, 1-3)=\boxed{(2, -2)}[/tex]

The answer is (2,-2).

Find the image of the given point under the given translation:

The rule of translation is (x+9, y - 3), P (-7, 1).

Here we need to add 9 from

x value is -7+9=2

y We need to subtract -3 from

y value is (1-3)=-2

So, P’=( 2,-2)

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Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]

Step-by-step explanation:

Given information

Number of coins = 24 coins

Total amount = $1.95

Dime = 10 cents = $0.1

Nickel = 5 cents = $0.05

Set variables

Let d be the number of dimes

Let n be the number of nickels

Set a system of equation

1) d + n = 24

2) 0.1d + 0.05n = 1.95

Multiply 10 on both sides of 2) equation

0.1d · 10 + 0.05n · 10 = 1.95 · 10

d + 0.5n = 19.5

Current system

1) d + n = 24

2) d + 0.5n = 19.5

Subtract 2) equation from the 1) equation

(d + n) - (d + 0.5n) = (24) - (19.5)

Expand the parenthesis

d + n - d - 0.5n = 24 - 19.5

Combine like terms

d - d + n - 0.5n = 4.5

0.5n = 4.5

Divide 0.5 on both sides

0.5n / 0.5 = 4.5 / 0.5

[tex]\Large\boxed{n=9}[/tex]

Substitute the n value into one of the equations to find the d value

d + n = 24

d + (9) = 24

d = 24 - 9

[tex]\Large\boxed{d=15}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

This is your answer!

Step-by-step explanation:

Answer: 9 diagonals

Step-by-step explanation:

Answer:

X=36

Step-by-step explanation:

2x + 3x=5x

if given figure is 180 then

5x=180

X=180/5

X=36